FRM Exam Part II · The Evolution of Stress Testing Counterparty Exposures

Counterparty Exposure Metrics: EE, PFE and EPE Explained

Updated 11 October 2026 · Fact-checked

Counterparty exposure metrics measure what you could lose if a counterparty defaults. Current exposure is today's replacement cost, floored at zero. Expected exposure (EE) is the average positive exposure at a future date. PFE is a high percentile of that distribution. EPE is the time-average of EE. Stress shifts all of them upward.

Understand Counterparty Exposure Metrics: EE, PFE and EPE

When a bank trades an OTC derivative, the contract value moves with markets. If the value is positive to you, the counterparty owes you. If it defaults, you lose that amount (before recovery). If the value is negative, you still owe, so your loss from the default is zero. So exposure is always max(V, 0).

Today's exposure is known. It is the current exposure (CE): max(V, 0), the replacement cost if the counterparty defaulted now. Future exposure is not known. You model it by simulating the risk factors (rates, FX, equity, credit spreads) and revaluing the trades at each future date. This gives a distribution of exposure at each date.

From that distribution you take summary measures. Expected exposure (EE) is the mean of the positive exposure at a date. Potential future exposure (PFE) is a high percentile (often 95% or 97.5%, sometimes 99%) of the same distribution at that date. PFE answers: how bad could it get at a given confidence level? It is used for limits. EE is an average, so it is used for pricing, such as CVA.

Two time-based summaries follow. Expected positive exposure (EPE) is the average of EE over a time horizon, usually one year. It is a single number. Peak exposure (or maximum PFE) is the highest PFE across the dates. Basel also uses effective EE, which forces EE to be non-decreasing over time, and effective EPE, the average of effective EE over the first year or until the longest maturity if shorter.

Stress changes these numbers. Stress scenarios move risk factors sharply, so exposures rise on trades that gain value. Stress can also raise volatility, cut collateral value, lengthen the margin period of risk, and create wrong-way risk, where exposure rises just as the counterparty's credit quality falls. Under stress, PFE usually rises more than EE, because the tail of the distribution moves most. Stressed EPE is also used in regulatory capital calibration.

Key formulas to remember

Current exposure: CE = max(V, 0); V is the netted mark-to-market value of the trades with the counterparty today. Zero if you owe the counterparty.
Exposure at future date t: E(t) = max(V(t), 0); V(t) is a random value at date t, so E(t) has a distribution.
Expected exposure: EE(t) = mean of E(t) = average of max(V(t), 0) across scenarios; Average includes zeros from scenarios where V is negative. Do not average only the positive paths.
Potential future exposure: PFE(t) = the α-percentile of E(t), e.g. 95% or 99%; Choose the percentile the question gives. PFE is not an average.
Expected positive exposure: EPE = (1 ÷ T) × ∫ EE(t) dt ≈ Σ EE(tᵢ) × Δtᵢ ÷ T; A time-weighted average of EE. With equal time steps it is the simple average of the EE values.
Effective EE: Effective EE(tₖ) = max(Effective EE(tₖ₋₁), EE(tₖ)); Non-decreasing in time. Captures rollover of short-dated trades.
Effective EPE: Effective EPE = time-average of Effective EE over the first year (or to maturity of the longest trade if under one year); Basel measure used in exposure at default for internal model method.
Peak exposure: Peak PFE = max over t of PFE(t); Used for limit monitoring. It can fall at a different date from the peak EE.

How to solve Counterparty Exposure Metrics: EE, PFE and EPE questions

Use this method for any question that gives exposure numbers, scenarios or a description of a stress and asks you to compute or interpret a metric.

1Identify which metric is asked: CE, EE, PFE, EPE, effective EPE or peak PFE. Note the date, percentile and time horizon.
2Check netting. If a netting agreement applies, exposure is max of the net value, not the sum of positive trade values. Apply collateral if given.
3Convert values to exposure with max(V, 0). Set negative values to zero before averaging or ranking.
4For EE, average the exposures across all scenarios, including zeros. For PFE, rank the exposures and read the percentile.
5For EPE, average EE over time, weighting by time step length. For effective EPE, first make EE non-decreasing, then average.
6Under stress, state the direction: which risk factors move, whether collateral, margin period of risk or wrong-way risk change, and which metric moves most (usually PFE).
7Check units and interpretation: EE is for pricing and capital, PFE is for limits. Match the answer to the stated use.

Quickest way: Floor, rank, average

When to use it: Numeric questions with a short list of scenario values or an EE profile over a few dates.

Floor every value at zero first.
For EE: add the floored values and divide by the number of scenarios.
For PFE: sort the floored values and pick the one at the percentile. With 20 scenarios, the 95th percentile is the 19th smallest value, the second largest. Follow the convention given.
For EPE: average the EE values by date, weighting by time step if steps are unequal.
For effective EE: take a running maximum before averaging.
For a stress question, eliminate options that say EE falls or that PFE is below EE.

Common mistakes in Counterparty Exposure Metrics: EE, PFE and EPE

Averaging only the positive scenarios when computing EE.
The word 'positive' in EPE suggests ignoring losses.
Fix: Floor at zero but keep every scenario in the denominator. Zero-exposure paths count.
Treating PFE and EE as the same thing or saying PFE is the average.
Both are described as future exposure.
Fix: EE is the mean, PFE is a percentile. PFE is at least as large as EE for the same date when the percentile is high.
Calling EPE a point-in-time measure.
EE and EPE look alike.
Fix: EE is per date. EPE is the time-average of EE over a horizon, usually one year.
Skipping netting and summing positive trade values.
Students compute each trade's exposure in isolation.
Fix: Under a legally enforceable netting agreement, net the trade values first, then floor the total at zero.
Forgetting the effective EE running maximum.
Students average raw EE when the question asks for effective EPE.
Fix: Take the running maximum of EE over time, then average over the first year.
Assuming stress lowers exposure for a hedged portfolio, or that stress affects EE and PFE equally.
Ignoring tail behaviour, collateral lag and wrong-way risk.
Fix: Stress moves the tail most, so PFE rises more than EE. Collateral, margin period of risk and wrong-way risk can all worsen exposure.

Worked examples

Example 1

A bank models a swap with a counterparty at one future date using 10 equally likely scenarios. The mark-to-market values (USD million) are: -4, -1, 0, 2, 3, 5, 6, 8, 10, 12. Compute (a) the expected exposure and (b) the 90% PFE, taking the 90th percentile as the 9th smallest exposure.

Show the solution

Floor at zero: 0, 0, 0, 2, 3, 5, 6, 8, 10, 12.
EE = sum ÷ 10. Sum = 2 + 3 + 5 + 6 + 8 + 10 + 12 = 46.
EE = 46 ÷ 10 = 4.6.
Sorted exposures are already in order. The 9th smallest is 10, so the 90% PFE = 10.

Answer: EE = USD 4.6 million; 90% PFE = USD 10 million.

Example 2

A bank's EE profile for a portfolio at quarterly dates is: 3M USD 6 million, 6M USD 9 million, 9M USD 8 million, 12M USD 5 million. Compute the effective EPE over one year using equal time steps, and say what happens to the figure if stress raises each EE by 20%.

Show the solution

Effective EE is the running maximum: 3M = 6; 6M = max(6, 9) = 9; 9M = max(9, 8) = 9; 12M = max(9, 5) = 9.
Average with equal steps: (6 + 9 + 9 + 9) ÷ 4 = 33 ÷ 4 = 8.25.
Under a 20% rise in each EE: 7.2, 10.8, 9.6, 6.0. Running maximum: 7.2, 10.8, 10.8, 10.8.
Stressed effective EPE = (7.2 + 10.8 + 10.8 + 10.8) ÷ 4 = 39.6 ÷ 4 = 9.9.
Check: 8.25 × 1.2 = 9.9, so it scales by 20% because every EE scales uniformly.

Answer: Effective EPE = USD 8.25 million; after the 20% stress it is USD 9.9 million.

Exam tips

Read the metric name carefully. Questions often swap EE for PFE or EPE in the options to test whether you know mean versus percentile versus time-average.
Always floor at zero before averaging or ranking. Many numeric traps use negative values.
For stress questions, think direction first: PFE and peak exposure rise most, and wrong-way risk can make exposure and default probability rise together.
Match use to metric: PFE for limits and credit appetite, EE for CVA pricing, effective EPE for Basel exposure at default.
If the question mentions netting or collateral, apply them before computing any metric.

Practice questions from The Evolution of Stress Testing Counterparty Exposures

Counterparty Exposure Metrics: EE, PFE and EPE: frequently asked questions

What is the difference between expected exposure and potential future exposure?

EE is the average of positive exposure at a future date. PFE is a high percentile of the same exposure distribution at that date, such as 95% or 99%. EE is used for pricing and capital, PFE for setting limits.

How is EPE different from PFE?

EPE is a time-average of EE over a horizon, usually one year, so it is one number. PFE is a percentile at each date, and you can take the maximum across dates as peak PFE. EPE is an average, PFE is a tail measure.

How do I calculate potential future exposure in FRM Part II?

Floor the simulated values at zero, rank the exposures at the date, and read the stated percentile. Apply netting and collateral first. Use the percentile convention in the question.

How does stress change counterparty exposure metrics?

Stress shifts risk factors, raises volatility and can weaken collateral or lengthen the margin period of risk. All metrics tend to rise, with PFE rising the most. Wrong-way risk can raise exposure when the counterparty is weakest.